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Solving MAXSAT and Weighted MAXSAT Problems Using BranchandCut
, 1998
"... We describe a branch and cut algorithm for both MAXSAT and weighted MAXSAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. W ..."
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Cited by 5 (2 self)
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We describe a branch and cut algorithm for both MAXSAT and weighted MAXSAT. This algorithm uses the GSAT procedure as a primal heuristic. At each nodewe solve a linear programming (LP) relaxation of the problem. Two styles of separating cuts are added: resolution cuts and odd cycle inequalities. We compare our algorithm to an extension of the Davis Putnam Loveland (EDPL) algorithm and a SemiDefinite Programming (SDP) approach. Our algorithm is more effective than EDPL on some problems, notably MAX2SAT. EDPL and SDP are more effective on some other classes of problems.
Approximations and Randomization to Boost CSP Techniques
 Annals of Operations Research
, 2004
"... Abstract. In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for sol ..."
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Abstract. In recent years we have seen an increasing interest in combining constraint satisfaction problem (CSP) formulations and linear programming (LP) based techniques for solving hard computational problems. While considerable progress has been made in the integration of these techniques for solving problems that exhibit a mixture of linear and combinatorial constraints, it has been surprisingly difficult to successfully integrate LPbased and CSPbased methods in a purely combinatorial setting. Our approach draws on recent results on approximation algorithms based on LP relaxations and randomized rounding techniques, with theoretical guarantees, as well on results that provide evidence that the runtime distributions of combinatorial search methods are often heavytailed. We propose a complete randomized backtrack search method for combinatorial problems that tightly couples CSP propagation techniques with randomized LPbased approximations. We present experimental results that show that our hybrid CSP/LP backtrack search method outperforms the pure CSP and pure LP strategies on instances of a hard combinatorial problem. 1.
C.: Quality of LPbased approximations for highly combinatorial problems
 In: International Conference on Principles and Practice of Constraint Programming (CP
, 2004
"... Abstract. We study the quality of LPbased approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in t ..."
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Cited by 3 (0 self)
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Abstract. We study the quality of LPbased approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in the solution integrality of the relaxation. The solution quality of approximation schemes degrades substantially near phase transition boundaries. Our findings are consistent over a range of LPbased approximation schemes. We also provide results on the extent to which LP relaxations can provide a global perspective of the search space and therefore be used as a heuristic to guide a complete solver.
A Hybrid Genetic Algorithm for the Satisfiability Problem
"... This paper introduces a hybrid genetic algorithm for the satisfiability problem (SAT). This algorithm, called GASAT, incorporates local search within the genetic framework. GASAT relays on a problem specific crossover operator to create new solutions, that are improved by a tabu search procedure. Th ..."
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Cited by 3 (0 self)
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This paper introduces a hybrid genetic algorithm for the satisfiability problem (SAT). This algorithm, called GASAT, incorporates local search within the genetic framework. GASAT relays on a problem specific crossover operator to create new solutions, that are improved by a tabu search procedure. The performance of GASAT is assessed using a set of wellknown benchmarks. Comparisons with stateoftheart SAT algorithms show that GASAT gives competitive results.
Protein Interaction Inference as a MAXSAT Problem
"... Discovering interacting proteins is essential for understanding protein functions in a systematic fashion. However, high throughput interaction data are inherently noisy and only cover a small portion of the interactom. The question can we infer useful proteinprotein interaction information from t ..."
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Cited by 2 (1 self)
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Discovering interacting proteins is essential for understanding protein functions in a systematic fashion. However, high throughput interaction data are inherently noisy and only cover a small portion of the interactom. The question can we infer useful proteinprotein interaction information from those high throughput data arises.
(0,±1) Ideal Matrices
 Mathematical Programming, Series A
, 1996
"... A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of finding a satisfactory characterization of those matrices which are minimally nonideal is a well known open problem. An outstanding result toward the solution of this pr ..."
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A (0; 1) matrix A is said to be ideal if all the vertices of the polytope Q(A) = fx : Ax 1; 0 x 1g are integral. The issue of finding a satisfactory characterization of those matrices which are minimally nonideal is a well known open problem. An outstanding result toward the solution of this problem, due to Alfred Lehman, is the description of crucial properties of minimally nonideal matrices. In this paper we consider the extension of the notion of ideality to (0; \Sigma1) matrices. By means of a standard transformation, we associate with any (0; \Sigma1) matrix A a suitable (0; 1) matrix D(A). Then we introduce the concept of disjoint completion A + of a (0; \Sigma1) matrix A and we show that A is ideal if and only if D(A + ) is ideal. Moreover, we introduce a suitable concept of a minimally nonideal (0; \Sigma1) matrix and we prove a Lehmantype characterization of minimally nonideal (0; \Sigma1) matrices. 1 Introduction Let A be a (0; \Sigma1) matrix whose sets of ...